[tex]\sqrt{x+2014}+\sqrt{2015-x}-\sqrt{2014-x}=\sqrt{y+2014}+\sqrt{2015-y}-\sqrt{2014-y}[/tex]
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[tex]\Leftrightarrow \sqrt{x+2014}-\sqrt{y+2014}+\sqrt{2015-x}-\sqrt{2015-y}-\sqrt{2014-x}+\sqrt{2014-y}=0\\ \Leftrightarrow \frac{x+2014-y-2014}{\sqrt{x+2014}+\sqrt{y+2014}}+\frac{2015-x-2015+y}{\sqrt{2015-x}+\sqrt{2015-y}}-\frac{2014-x+2014+y}{\sqrt{2014-x}+\sqrt{2014-y}}=0\\ \Leftrightarrow \frac{x-y}{\sqrt{2014+x}+\sqrt{y+2014}}-\frac{x-y}{\sqrt{2015-x}+\sqrt{2015-y}}+\frac{x-y}{\sqrt{2014-x}+\sqrt{2014-y}}=0\\ \Leftrightarrow (x-y)(\frac{1}{\sqrt{2014+x}+\sqrt{y+2014}}-\frac{1}{\sqrt{2015-x}+\sqrt{2015-y}}-\frac{1}{\sqrt{2014-x}+\sqrt{2014-y}})=0\\ \Rightarrow x-y=0\Leftrightarrow x=y(dpcm)[/tex]
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